       Newton's Method Help [0/1]

• To: mathgroup at smc.vnet.net
• Subject: [mg5072] Newton's Method Help [0/1]
• From: rligeski at webbernet.net
• Date: Fri, 25 Oct 1996 22:48:17 -0400
• Organization: WebNet
• Sender: owner-wri-mathgroup at wolfram.com

```Hello,

In my calculus class we just began using Mathematica for Newtons method.
We were given a lab to do involving the method, but there is a special program
so we can use Newton[] and NewtonTable[].  The former takes the equation with
an initial guess goes through a certain number of iterations and then graphs
each of them.  The latter does the same thing except it puts it into a table
format instead of graphing.  I do understand Newtons method.  We were given 2
problems that no one in my class can get.  He won't help us because he thinks
we should be able to do it.  I was wondering if someone could help me with the
problems.  They are:

1.  Find a polynomial F so that Newton's method fails to converge in the
following way for X(sub 0)=1.  The first iteration gives X(sub 1)= -1, the next
X(sub 2)= -2, and X(sub 3)=X(sub 0] the starting point.  Assume F(1)=1,
F(-1)=2, and F(-2)=3

2.  Find a polynomial F which fails as above but which also has one root
between -1 and 1 at 0; that is in addition to values given above, F(0)=0

The teacher did give us a hint, he said sketch it first.  I did this but
don't know how to use Mathematica well enough to do this.  I also searched the
Mathematica website but that did not help.  I am going to include the notebook
that we used in school, because this is not standard.  I would appreciate it if
someone would try to help me.

Thank You,
Brian Ligeski

```

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